...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >An error estimator for separated representations of highly multidimensional models
【24h】

An error estimator for separated representations of highly multidimensional models

机译：用于高度多维模型的分离表示的误差估计器

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Fine modeling of the structure and mechanics of materials from the nanometric to the micrometric scales uses descriptions ranging from quantum to statistical mechanics. Most of these models consist of a partial differential equation defined in a highly multidimensional domain (e.g. Schrodinger equation, Fokker-Planck equations among many others). The main challenge related to these models is their associated curse of dimensionality. We proposed in some of our former works a new strategy able to circumvent the curse of dimensionality based on the use of separated representations (also known as finite sums decomposition). This technique proceeds by computing at each iteration a new sum that consists of a product of functions each one defined in one of the model coordinates. The issue related to error estimation has never been addressed. This paper presents a first attempt on the accuracy evaluation of such a kind of discretization techniques.
机译：从纳米尺度到微米尺度的材料结构和力学的精细建模，使用从量子力学到统计力学的描述。这些模型中的大多数都由在高度多维域中定义的偏微分方程组成（例如Schrodinger方程，Fokker-Planck方程等）。与这些模型相关的主要挑战是它们与维数有关的诅咒。我们在一些以前的作品中提出了一种新策略，该策略可以基于分离表示的使用来规避维数的诅咒（也称为有限和分解）。通过在每次迭代中计算一个新的总和来进行这项技术，该新的总和由在模型坐标之一中定义的每个函数的乘积组成。与错误估计有关的问题从未得到解决。本文提出了这种离散化技术的准确性评估的首次尝试。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号